Is the Mona Lisa’s ambiguous smile happy or sad? Does hippocampus place cell discharge signal current or recollected position, “here” or “there”? Despite the presence of parallel discrete for-purpose neural circuits, many neural circuits nonetheless process conflicting types of information, making monolithic ideas about neural circuit function inadequate. Similar to how low spatial frequencies in the Mona Lisa reveal a smile whereas high spatial frequencies do not, we observe that hippocampal CA1 principal cell discharge associated with slow (30 Hz) gamma oscillations encodes information about “there” remote recollected locations, and mid-frequency 70-Hz associated discharge encodes information about current position “here.” Different classes of information including location, spatial reference frame, environment identity, and task are all conjointly encoded within the same hippocampal neuronal network ensemble discharge, and we present evidence that differentially filtering this functionally-mixed activity at distinct temporal frequencies and spatial domains enables demixing, such that specific types of information can be extracted and used for purposeful cognition. I will consider computational, neurophysiological and biochemical evidence in this survey of the mechanisms of cognitive control that our research program has identified. I propose that specific synaptic compartments and functionally-distinct inhibitory interneuron classes provide mechanisms for the dynamic control of the information processing and extraction.